Global solutions of Yang–Mills–Higgs systems on four-dimensional Minkowski space: I. Existence

The existence of global solutions to the Cauchy problem for Yang–Mills–Higgs systems in the temporal gauge is examined. The results apply to the self-coupling of the Higgs field. Results from other works are strengthened.     

Crystallographic classes on the Minkowski space R 1,2. II. Tables of groups

For the Minkowski spaces, the traditional definition of a crystallographic group yields only trivial groups that are isomorphic to the Euclidean groups. In this article, we use a weaker definition (the topological discreteness). We classify the isomorphism types of the groups in the six crystallographic classes in the 3-dimensional Minkowski space: three classes are determined by the unimodular subgroups of the general Lorentz group, and the other three classes, by the subgroups unimodular in isotropic coordinates.     

Global existence of solutions to reaction–diffusion systems without conditions on the nonlinearities growth

It is well known that, for reaction–diffusion systems, if the nonlinearities grow faster than a polynomial, nothing seems to be known for instance. The purpose of this paper is to give sufficient conditions guaranteeing global existence, uniqueness and uniform boundedness of solutions for coupled reaction–diffusion equations without condition growth on the reactions terms f and g in case f + g ≠ 0. These systems possess many and various applications in physics as the diffusion of the Phosphorus in the Silicone or some models describing some nuclear reactions; there have also been other applications in chemistry and biology. Our techniques are based on the Lyapunov functional methods. Copyright © 2010 John Wiley & Sons, Ltd.     

Global existence of small solutions for quadratic quasilinear Klein-Gordon systems in two space dimensions

Consider a quasi-linear system of two Klein-Gordon equations with masses m₁, m₂. We prove that when m₁≠2m₂ and m₂≠2m₁, such a system has global solutions for small, smooth, compactly supported Cauchy data. This extends a result proved by Sunagawa (J. Differential Equations 192 (2) (2003) 308) in the semi-linear case. Moreover, we show that global existence holds true also when m₁=2m₂ and a convenient null condition is satisfied by the nonlinearities.     

Global classical solutions to a kind of quasilinear hyperbolic systems in several space variables

For a kind of quasilinear hyperbolic systems in several space variables whose coefficient matrices commute each other, by means of normalized coordinates, formulas of wave decomposition and pointwise decay estimates, the global existence of classical solution to the Cauchy problem for small and decaying initial data is obtained, under hypotheses of weak linear degeneracy and weakly strict hyperbolicity.     

Global boundedness of solutions to a reaction–diffusion system

We obtain in this paper the global boundedness of solutions to a Fujita‐type reaction–diffusion system. This global boundedness results from diffusion effect, homogeneous Dirichlet boundary value conditions and appropriate reactions. Copyright © 1999 John Wiley & Sons, Ltd.     

Global weak solutions to the Cauchy problem of compressible Navier–Stokes–Vlasov–Fokker–Planck equations

A fluid–particles system of the compressible Navier‐Stokes equations and Vlasov‐Fokker‐Planck equation (including the case of Vlasov equation) in three‐dimensional space is considered in this paper. The coupling arises from a drag force exerted by the fluid onto the particles. We study a Cauchy problem with large data, and establish the existence of global weak solutions through an approximation scheme, energy estimates, and weak convergence. Copyright © 2016 John Wiley & Sons, Ltd.     

Some properties of solutions of nonlocal elliptic problems in the space of generalized functions

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 11, pp. 1487–1494, November, 1989.     

Hardy space of solutions of elliptic systems on the plane

The space indicated in the title is introduced and studied. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 57, Suzdal Conference–2006, Part 3, 2008.     

Global classical solutions of viscous liquid–gas two‐phase flow model

In this paper, we consider the global existence and uniqueness of the classical solutions for the three‐dimensional where the existence of global classical solutions to the compressible Navier–Stokes equations was obtained by using the continuity methods under the assumption that the initial energy is sufficiently small. Copyright © 2012 John Wiley & Sons, Ltd.     

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.